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Class Notes Date: 10.1 – CONGRUENT TRIANGLE POSTULATES AND THEOREMS (SSS, SAS, ASA, AAS, and HL) Side – Side – Side (SSS) Prove B AB DE BC EF E AC DF A C F D then ∆ABC ∆DEF by SSS Side – Angle – Side (SAS) Prove B A D E A C AC DF D F AB DE then ∆ABC ∆DEF by SAS Angle – Side – Angle (ASA) Prove B A C AD CD Note that the side marked is between the two angles. BDA BDC then ∆ABD ∆CBD by A C D Angle – Angle – Side (AAS) Prove A B D B BCA DCE C AC EC then ∆ABC ∆EDC by D ASA AAS E Page 1 Class Notes Date: Hypotenuse – Leg (HL) – must be a right triangle; must state right angle in proof A Prove D mC=90°, mF=90° AB DE BC EF C B F then ∆ABC ∆DEF by E HL Can the triangles be proved congruent? If so, name the postulate (SSS, SAS, or ASA) or theorem (AAS or HL) that would prove the triangles congruent. If not, write NONE. You must use the markings shown. The only markings that can be added are shared sides or vertical angles. 1) 2) 3) HL AAS SAS 4) 5) 6) SSS HL AAS 7) 8) 9) SAS ASA NONE 10) 11) ASA 12) AAS AAS Page 2 Class Notes Date: 13) 14) 15) AAS NONE SSS What additional congruence statement is needed to prove the triangles congruent by the indicated postulate or theorem? K Given: ∆JKM and ∆LKM KM KM 13) JK LK , JM LM by SSS J L 14) 1 2 , KM KM by AAS JM LM 15) J L , 1 2 by ASA JM LM 16) JK LK , J L by SAS Given: ∆OPQ and ∆SRQ 1 2 M J L P O OQ SQ 17) OP SR , PQ RQ by SSS 1 Q OQ SQ 18) O S , 1 2 by ASA 1 2 19) OQ SQ , PQ RQ by SAS O S 20) PQ RQ , 1 2 by AAS 2 R S Use the given information to determine if the triangles below are congruent. If so, which congruence postulate or theorem would you use? 21) Given: C is the midpoint of SU . DU KS Is DUC KSC ? NO D C U S K Page 3